LMFDB - Embedded newform 1134.2.g.l.487.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1134 = 2 \cdot 3^{4} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3$ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1134.487
Dual form			1134.2.g.l.163.2

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.296790 + 0.514055i) q^{5} +(-2.25729 - 1.38008i) q^{7} +1.00000 q^{8} +(0.296790 - 0.514055i) q^{10} +(-0.296790 + 0.514055i) q^{11} +2.51459 q^{13} +(-0.0665372 + 2.64491i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.46050 + 2.52967i) q^{17} +(2.69076 + 4.66053i) q^{19} -0.593579 q^{20} +0.593579 q^{22} +(2.23025 + 3.86291i) q^{23} +(2.32383 - 4.02499i) q^{25} +(-1.25729 - 2.17770i) q^{26} +(2.32383 - 1.26483i) q^{28} -6.19436 q^{29} +(3.93346 - 6.81296i) q^{31} +(-0.500000 + 0.866025i) q^{32} +2.92101 q^{34} +(0.0394951 - 1.56997i) q^{35} +(0.500000 + 0.866025i) q^{37} +(2.69076 - 4.66053i) q^{38} +(0.296790 + 0.514055i) q^{40} -0.273346 q^{41} +11.1623 q^{43} +(-0.296790 - 0.514055i) q^{44} +(2.23025 - 3.86291i) q^{46} +(6.08113 + 10.5328i) q^{47} +(3.19076 + 6.23049i) q^{49} -4.64766 q^{50} +(-1.25729 + 2.17770i) q^{52} +(-4.02704 + 6.97504i) q^{53} -0.352336 q^{55} +(-2.25729 - 1.38008i) q^{56} +(3.09718 + 5.36447i) q^{58} +(4.32383 - 7.48910i) q^{59} +(3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 + 1.29264i) q^{65} +(0.956906 - 1.65741i) q^{67} +(-1.46050 - 2.52967i) q^{68} +(-1.37938 + 0.750780i) q^{70} +14.4107 q^{71} +(3.95691 - 6.85356i) q^{73} +(0.500000 - 0.866025i) q^{74} -5.38151 q^{76} +(1.37938 - 0.750780i) q^{77} +(4.62422 + 8.00938i) q^{79} +(0.296790 - 0.514055i) q^{80} +(0.136673 + 0.236725i) q^{82} +7.70175 q^{83} -1.73385 q^{85} +(-5.58113 - 9.66679i) q^{86} +(-0.296790 + 0.514055i) q^{88} +(6.21780 + 10.7695i) q^{89} +(-5.67617 - 3.47033i) q^{91} -4.46050 q^{92} +(6.08113 - 10.5328i) q^{94} +(-1.59718 + 2.76639i) q^{95} -11.7339 q^{97} +(3.80039 - 5.87852i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 3 q^{2} - 3 q^{4} - q^{5} + 2 q^{7} + 6 q^{8} - q^{10} + q^{11} - 16 q^{13} - 4 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} + 2 q^{20} - 2 q^{22} + 7 q^{23} + 2 q^{25} + 8 q^{26} + 2 q^{28} - 10 q^{29}+ \cdots + 12 q^{98}+O(q^{100})$ 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 2 * q^7 + 6 * q^8 - q^10 + q^11 - 16 * q^13 - 4 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 + 2 * q^20 - 2 * q^22 + 7 * q^23 + 2 * q^25 + 8 * q^26 + 2 * q^28 - 10 * q^29 + 20 * q^31 - 3 * q^32 - 8 * q^34 + 13 * q^35 + 3 * q^37 - 3 * q^38 - q^40 + 12 * q^43 + q^44 + 7 * q^46 + 9 * q^47 - 4 * q^50 + 8 * q^52 - 15 * q^53 - 26 * q^55 + 2 * q^56 + 5 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 4 * q^68 - 23 * q^70 - 14 * q^71 + 19 * q^73 + 3 * q^74 + 6 * q^76 + 23 * q^77 + 5 * q^79 - q^80 + 4 * q^83 + 4 * q^85 - 6 * q^86 + q^88 + 9 * q^89 - 46 * q^91 - 14 * q^92 + 9 * q^94 + 4 * q^95 - 56 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$ .

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	0.924727	−	0.380630i	$-0.124293\pi$
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	−0.791999	+	0.610522i	$0.790960\pi$
$6$		0			0
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.296790	−	0.514055i	0.0938531	−	0.162558i
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	−0.907294	−	0.420497i	$-0.861856\pi$
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	0.817808	+	0.575491i	$0.195189\pi$
$12$		0			0
$13$	2.51459			0.697422			0.348711	−	0.937230i	$-0.386620\pi$
$13$	2.51459			0.697422			0.348711	+	0.937230i	$0.386620\pi$
$14$	−0.0665372	+	2.64491i	−0.0177828	+	0.706883i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.46050	+	2.52967i	−0.354224	+	0.613535i	−0.986985	−	0.160813i	$-0.948588\pi$
$17$	−1.46050	+	2.52967i	−0.354224	+	0.613535i	0.632760	+	0.774348i	$0.281922\pi$
$18$		0			0
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	0.989976	+	0.141236i	$0.0451077\pi$
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	−0.372674	+	0.927962i	$0.621559\pi$
$20$	−0.593579			−0.132728
$21$		0			0
$22$	0.593579			0.126552
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	0.999203	−	0.0399086i	$-0.0127067\pi$
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	−0.534164	+	0.845381i	$0.679373\pi$
$24$		0			0
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$	−1.25729	−	2.17770i	−0.246576	−	0.427082i
$27$		0			0
$28$	2.32383	−	1.26483i	0.439163	−	0.239031i
$29$	−6.19436			−1.15026			−0.575132	−	0.818061i	$-0.695049\pi$
$29$	−6.19436			−1.15026			−0.575132	+	0.818061i	$0.695049\pi$
$30$		0			0
$31$	3.93346	−	6.81296i	0.706471	−	1.22364i	−0.259687	−	0.965693i	$-0.583620\pi$
$31$	3.93346	−	6.81296i	0.706471	−	1.22364i	0.966158	−	0.257951i	$-0.0830472\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.92101			0.500949
$35$	0.0394951	−	1.56997i	0.00667590	−	0.265373i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	2.69076	−	4.66053i	0.436498	−	0.756038i
$39$		0			0
$40$	0.296790	+	0.514055i	0.0469266	+	0.0812792i
$41$	−0.273346			−0.0426895			−0.0213448	−	0.999772i	$-0.506795\pi$
$41$	−0.273346			−0.0426895			−0.0213448	+	0.999772i	$0.506795\pi$
$42$		0			0
$43$	11.1623			1.70223			0.851114	−	0.524981i	$-0.175928\pi$
$43$	11.1623			1.70223			0.851114	+	0.524981i	$0.175928\pi$
$44$	−0.296790	−	0.514055i	−0.0447427	−	0.0774967i
$45$		0			0
$46$	2.23025	−	3.86291i	0.328833	−	0.569555i
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.843377	+	0.537323i	$0.180564\pi$
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.0436467	+	0.999047i	$0.486102\pi$
$48$		0			0
$49$	3.19076	+	6.23049i	0.455822	+	0.890071i
$50$	−4.64766			−0.657279
$51$		0			0
$52$	−1.25729	+	2.17770i	−0.174355	+	0.301992i
$53$	−4.02704	+	6.97504i	−0.553157	+	0.958096i	0.444888	+	0.895586i	$0.353244\pi$
$53$	−4.02704	+	6.97504i	−0.553157	+	0.958096i	−0.998044	+	0.0625092i	$0.980090\pi$
$54$		0			0
$55$	−0.352336			−0.0475090
$56$	−2.25729	−	1.38008i	−0.301644	−	0.184421i
$57$		0			0
$58$	3.09718	+	5.36447i	0.406679	+	0.704389i
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	−0.434325	−	0.900756i	$-0.643013\pi$
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	0.997240	−	0.0742412i	$-0.0236535\pi$
$60$		0			0
$61$	3.32383	+	5.75705i	0.425573	+	0.737114i	0.996474	−	0.0839050i	$-0.0267392\pi$
$61$	3.32383	+	5.75705i	0.425573	+	0.737114i	−0.570901	+	0.821019i	$0.693406\pi$
$62$	−7.86693			−0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	0.746304	+	1.29264i	0.0925676	+	0.160332i
$66$		0			0
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	−0.801635	−	0.597814i	$-0.796036\pi$
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	0.918540	+	0.395329i	$0.129369\pi$
$68$	−1.46050	−	2.52967i	−0.177112	−	0.306767i
$69$		0			0
$70$	−1.37938	+	0.750780i	−0.164867	+	0.0897353i
$71$	14.4107			1.71023			0.855117	−	0.518435i	$-0.173485\pi$
$71$	14.4107			1.71023			0.855117	+	0.518435i	$0.173485\pi$
$72$		0			0
$73$	3.95691	−	6.85356i	0.463121	−	0.802149i	−0.535994	−	0.844222i	$-0.680063\pi$
$73$	3.95691	−	6.85356i	0.463121	−	0.802149i	0.999115	+	0.0420732i	$0.0133963\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−5.38151			−0.617302
$77$	1.37938	−	0.750780i	0.157195	−	0.0855593i
$78$		0			0
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	0.999722	+	0.0235607i	$0.00750031\pi$
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	−0.479457	+	0.877565i	$0.659166\pi$
$80$	0.296790	−	0.514055i	0.0331821	−	0.0574731i
$81$		0			0
$82$	0.136673	+	0.236725i	0.0150930	+	0.0261419i
$83$	7.70175			0.845377			0.422688	−	0.906275i	$-0.361087\pi$
$83$	7.70175			0.845377			0.422688	+	0.906275i	$0.361087\pi$
$84$		0			0
$85$	−1.73385			−0.188063
$86$	−5.58113	−	9.66679i	−0.601828	−	1.04240i
$87$		0			0
$88$	−0.296790	+	0.514055i	−0.0316379	+	0.0547984i
$89$	6.21780	+	10.7695i	0.659085	+	1.14157i	0.980853	+	0.194751i	$0.0623898\pi$
$89$	6.21780	+	10.7695i	0.659085	+	1.14157i	−0.321767	+	0.946819i	$0.604277\pi$
$90$		0			0
$91$	−5.67617	−	3.47033i	−0.595024	−	0.363790i
$92$	−4.46050			−0.465040
$93$		0			0
$94$	6.08113	−	10.5328i	0.627220	−	1.08638i
$95$	−1.59718	+	2.76639i	−0.163867	+	0.283826i
$96$		0			0
$97$	−11.7339			−1.19139			−0.595696	−	0.803210i	$-0.703124\pi$
$97$	−11.7339			−1.19139			−0.595696	+	0.803210i	$0.703124\pi$
$98$	3.80039	−	5.87852i	0.383897	−	0.593821i
$99$		0			0
$100$	2.32383	+	4.02499i	0.232383	+	0.402499i
$101$	−0.811379	+	1.40535i	−0.0807352	+	0.139837i	−0.903566	−	0.428449i	$-0.859060\pi$
$101$	−0.811379	+	1.40535i	−0.0807352	+	0.139837i	0.822831	+	0.568287i	$0.192393\pi$
$102$		0			0
$103$	−3.19076	−	5.52655i	−0.314395	−	0.544548i	0.664914	−	0.746920i	$-0.268468\pi$
$103$	−3.19076	−	5.52655i	−0.314395	−	0.544548i	−0.979309	+	0.202372i	$0.935135\pi$
$104$	2.51459			0.246576
$105$		0			0
$106$	8.05408			0.782282
$107$	−9.35447	−	16.2024i	−0.904331	−	1.56635i	−0.821813	−	0.569758i	$-0.807037\pi$
$107$	−9.35447	−	16.2024i	−0.904331	−	1.56635i	−0.0825182	−	0.996590i	$-0.526296\pi$
$108$		0			0
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	−0.926474	−	0.376359i	$-0.877176\pi$
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	0.789173	+	0.614171i	$0.210509\pi$
$110$	0.176168	+	0.305132i	0.0167970	+	0.0290932i
$111$		0			0
$112$	−0.0665372	+	2.64491i	−0.00628718	+	0.249921i
$113$	−12.3202			−1.15899			−0.579495	−	0.814976i	$-0.696750\pi$
$113$	−12.3202			−1.15899			−0.579495	+	0.814976i	$0.696750\pi$
$114$		0			0
$115$	−1.32383	+	2.29294i	−0.123448	+	0.213818i
$116$	3.09718	−	5.36447i	0.287566	−	0.498078i
$117$		0			0
$118$	−8.64766			−0.796082
$119$	6.78794	−	3.69459i	0.622249	−	0.338683i
$120$		0			0
$121$	5.32383	+	9.22115i	0.483985	+	0.838286i
$122$	3.32383	−	5.75705i	0.300926	−	0.521218i
$123$		0			0
$124$	3.93346	+	6.81296i	0.353235	+	0.611822i
$125$	5.72665			0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.746304	−	1.29264i	0.0654552	−	0.113372i
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	0.838929	−	0.544240i	$-0.183182\pi$
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	−0.890791	+	0.454414i	$0.849849\pi$
$132$		0			0
$133$	0.358071	−	14.2336i	0.0310487	−	1.23421i
$134$	−1.91381			−0.165328
$135$		0			0
$136$	−1.46050	+	2.52967i	−0.125237	+	0.216917i
$137$	1.26089	−	2.18393i	0.107725	−	0.186586i	−0.807123	−	0.590383i	$-0.798977\pi$
$137$	1.26089	−	2.18393i	0.107725	−	0.186586i	0.914848	+	0.403797i	$0.132310\pi$
$138$		0			0
$139$	−4.91381			−0.416784			−0.208392	−	0.978045i	$-0.566823\pi$
$139$	−4.91381			−0.416784			−0.208392	+	0.978045i	$0.566823\pi$
$140$	1.33988	+	0.819187i	0.113241	+	0.0692339i
$141$		0			0
$142$	−7.20535	−	12.4800i	−0.604659	−	1.04730i
$143$	−0.746304	+	1.29264i	−0.0624091	+	0.108096i
$144$		0			0
$145$	−1.83842	−	3.18424i	−0.152673	−	0.264437i
$146$	−7.91381			−0.654952
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	9.02558	+	15.6328i	0.739404	+	1.28069i	0.952764	+	0.303712i	$0.0982261\pi$
$149$	9.02558	+	15.6328i	0.739404	+	1.28069i	−0.213360	+	0.976974i	$0.568441\pi$
$150$		0			0
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	−0.897598	−	0.440815i	$-0.854690\pi$
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	0.830556	+	0.556936i	$0.188023\pi$
$152$	2.69076	+	4.66053i	0.218249	+	0.378019i
$153$		0			0
$154$	−1.33988	−	0.819187i	−0.107971	−	0.0660120i
$155$	4.66964			0.375075
$156$		0			0
$157$	3.30039	−	5.71644i	0.263400	−	0.456222i	−0.703743	−	0.710454i	$-0.748490\pi$
$157$	3.30039	−	5.71644i	0.263400	−	0.456222i	0.967143	+	0.254233i	$0.0818229\pi$
$158$	4.62422	−	8.00938i	0.367883	−	0.637192i
$159$		0			0
$160$	−0.593579			−0.0469266
$161$	0.296790	−	11.7977i	0.0233903	−	0.929785i
$162$		0			0
$163$	−2.99115	−	5.18082i	−0.234285	−	0.405793i	0.724780	−	0.688980i	$-0.241941\pi$
$163$	−2.99115	−	5.18082i	−0.234285	−	0.405793i	−0.959065	+	0.283188i	$0.908608\pi$
$164$	0.136673	−	0.236725i	0.0106724	−	0.0184851i
$165$		0			0
$166$	−3.85087	−	6.66991i	−0.298886	−	0.517685i
$167$	7.46050			0.577311			0.288656	−	0.957433i	$-0.406792\pi$
$167$	7.46050			0.577311			0.288656	+	0.957433i	$0.406792\pi$
$168$		0			0
$169$	−6.67684			−0.513603
$170$	0.866926	+	1.50156i	0.0664902	+	0.115164i
$171$		0			0
$172$	−5.58113	+	9.66679i	−0.425557	+	0.737086i
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.678562	−	0.734543i	$-0.737397\pi$
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.296851	−	0.954924i	$-0.595937\pi$
$174$		0			0
$175$	−10.8004	+	5.87852i	−0.816433	+	0.444375i
$176$	0.593579			0.0447427
$177$		0			0
$178$	6.21780	−	10.7695i	0.466044	−	0.807211i
$179$	−7.51819	+	13.0219i	−0.561936	+	0.973301i	0.435392	+	0.900241i	$0.356610\pi$
$179$	−7.51819	+	13.0219i	−0.561936	+	0.973301i	−0.997328	+	0.0730602i	$0.976723\pi$
$180$		0			0
$181$	−0.0861875			−0.00640627			−0.00320313	−	0.999995i	$-0.501020\pi$
$181$	−0.0861875			−0.00640627			−0.00320313	+	0.999995i	$0.501020\pi$
$182$	−0.167314	+	6.65087i	−0.0124021	+	0.492996i
$183$		0			0
$184$	2.23025	+	3.86291i	0.164416	+	0.284778i
$185$	−0.296790	+	0.514055i	−0.0218204	+	0.0377941i
$186$		0			0
$187$	−0.866926	−	1.50156i	−0.0633959	−	0.109805i
$188$	−12.1623			−0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	1.99115	+	3.44877i	0.144074	+	0.249544i	0.929027	−	0.370011i	$-0.120646\pi$
$191$	1.99115	+	3.44877i	0.144074	+	0.249544i	−0.784953	+	0.619555i	$0.787313\pi$
$192$		0			0
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	−0.961862	−	0.273534i	$-0.911808\pi$
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	0.717818	+	0.696230i	$0.245141\pi$
$194$	5.86693	+	10.1618i	0.421221	+	0.729576i
$195$		0			0
$196$	−6.99115	−	0.351971i	−0.499368	−	0.0251408i
$197$	−11.0584			−0.787875			−0.393938	−	0.919137i	$-0.628887\pi$
$197$	−11.0584			−0.787875			−0.393938	+	0.919137i	$0.628887\pi$
$198$		0			0
$199$	2.80924	−	4.86575i	0.199142	−	0.344924i	−0.749109	−	0.662447i	$-0.769518\pi$
$199$	2.80924	−	4.86575i	0.199142	−	0.344924i	0.948250	+	0.317523i	$0.102851\pi$
$200$	2.32383	−	4.02499i	0.164320	−	0.284610i
$201$		0			0
$202$	1.62276			0.114177
$203$	13.9825	+	8.54871i	0.981378	+	0.600002i
$204$		0			0
$205$	−0.0811263	−	0.140515i	−0.00566611	−	0.00981399i
$206$	−3.19076	+	5.52655i	−0.222311	+	0.385053i
$207$		0			0
$208$	−1.25729	−	2.17770i	−0.0871777	−	0.150996i
$209$	−3.19436			−0.220958
$210$		0			0
$211$	−19.3245			−1.33035			−0.665177	−	0.746686i	$-0.731644\pi$
$211$	−19.3245			−1.33035			−0.665177	+	0.746686i	$0.731644\pi$
$212$	−4.02704	−	6.97504i	−0.276578	−	0.479048i
$213$		0			0
$214$	−9.35447	+	16.2024i	−0.639459	+	1.10757i
$215$	3.31284	+	5.73801i	0.225934	+	0.391329i
$216$		0			0
$217$	−18.2814	+	9.95036i	−1.24102	+	0.675474i
$218$	2.86693			0.194173
$219$		0			0
$220$	0.176168	−	0.305132i	0.0118773	−	0.0205720i
$221$	−3.67257	+	6.36108i	−0.247044	+	0.427892i
$222$		0			0
$223$	−25.3245			−1.69585			−0.847927	−	0.530113i	$-0.822150\pi$
$223$	−25.3245			−1.69585			−0.847927	+	0.530113i	$0.822150\pi$
$224$	2.32383	−	1.26483i	0.155268	−	0.0845103i
$225$		0			0
$226$	6.16012	+	10.6696i	0.409765	+	0.709734i
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	−0.774957	−	0.632014i	$-0.782229\pi$
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	0.934819	+	0.355126i	$0.115562\pi$
$228$		0			0
$229$	4.64766	+	8.04999i	0.307126	+	0.531958i	0.977732	−	0.209855i	$-0.0672993\pi$
$229$	4.64766	+	8.04999i	0.307126	+	0.531958i	−0.670606	+	0.741814i	$0.733966\pi$
$230$	2.64766			0.174582
$231$		0			0
$232$	−6.19436			−0.406679
$233$	−0.0971780	−	0.168317i	−0.00636634	−	0.0110268i	0.862825	−	0.505503i	$-0.168693\pi$
$233$	−0.0971780	−	0.168317i	−0.00636634	−	0.0110268i	−0.869191	+	0.494476i	$0.835360\pi$
$234$		0			0
$235$	−3.60963	+	6.25206i	−0.235466	+	0.407840i
$236$	4.32383	+	7.48910i	0.281457	+	0.487499i
$237$		0			0
$238$	−6.59358	−	4.03123i	−0.427398	−	0.261306i
$239$	−13.6549			−0.883260			−0.441630	−	0.897197i	$-0.645600\pi$
$239$	−13.6549			−0.883260			−0.441630	+	0.897197i	$0.645600\pi$
$240$		0			0
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$	5.32383	−	9.22115i	0.342229	−	0.592758i
$243$		0			0
$244$	−6.64766			−0.425573
$245$	−2.25583	+	3.48937i	−0.144120	+	0.222928i
$246$		0			0
$247$	6.76615	+	11.7193i	0.430520	+	0.745682i
$248$	3.93346	−	6.81296i	0.249775	−	0.432623i
$249$		0			0
$250$	−2.86333	−	4.95943i	−0.181093	−	0.313662i
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$	−6.16731	−	10.6821i	−0.386972	−	0.670255i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.16372	+	7.21177i	0.259725	+	0.449858i	0.966168	−	0.257912i	$-0.0830346\pi$
$257$	4.16372	+	7.21177i	0.259725	+	0.449858i	−0.706443	+	0.707770i	$0.749701\pi$
$258$		0			0
$259$	0.0665372	−	2.64491i	0.00413442	−	0.164347i
$260$	−1.49261			−0.0925676
$261$		0			0
$262$	−0.593579	+	1.02811i	−0.0366715	+	0.0635168i
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	0.472586	+	0.881284i	$0.343320\pi$
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	−0.999508	+	0.0313704i	$0.990013\pi$
$264$		0			0
$265$	−4.78074			−0.293678
$266$	−12.5057	+	6.80672i	−0.766776	+	0.417347i
$267$		0			0
$268$	0.956906	+	1.65741i	0.0584524	+	0.101242i
$269$	5.00720	−	8.67272i	0.305294	−	0.528785i	−0.672033	−	0.740522i	$-0.734579\pi$
$269$	5.00720	−	8.67272i	0.305294	−	0.528785i	0.977327	+	0.211737i	$0.0679119\pi$
$270$		0			0
$271$	5.10457	+	8.84137i	0.310081	+	0.537075i	0.978380	−	0.206818i	$-0.0663106\pi$
$271$	5.10457	+	8.84137i	0.310081	+	0.537075i	−0.668299	+	0.743893i	$0.732977\pi$
$272$	2.92101			0.177112
$273$		0			0
$274$	−2.52179			−0.152347
$275$	1.37938	+	2.38915i	0.0831797	+	0.144071i
$276$		0			0
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	0.414271	+	0.910154i	$0.364037\pi$
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	−0.995352	+	0.0963074i	$0.969297\pi$
$278$	2.45691	+	4.25549i	0.147355	+	0.255227i
$279$		0			0
$280$	0.0394951	−	1.56997i	0.00236029	−	0.0938235i
$281$	−12.8027			−0.763746			−0.381873	−	0.924215i	$-0.624721\pi$
$281$	−12.8027			−0.763746			−0.381873	+	0.924215i	$0.624721\pi$
$282$		0			0
$283$	8.17617	−	14.1615i	0.486023	−	0.841816i	−0.513848	−	0.857881i	$-0.671781\pi$
$283$	8.17617	−	14.1615i	0.486023	−	0.841816i	0.999871	+	0.0160650i	$0.00511388\pi$
$284$	−7.20535	+	12.4800i	−0.427559	+	0.740553i
$285$		0			0
$286$	1.49261			0.0882598
$287$	0.617023	+	0.377240i	0.0364217	+	0.0222678i
$288$		0			0
$289$	4.23385	+	7.33325i	0.249050	+	0.431367i
$290$	−1.83842	+	3.18424i	−0.107956	+	0.186985i
$291$		0			0
$292$	3.95691	+	6.85356i	0.231560	+	0.401074i
$293$	−20.7778			−1.21385			−0.606926	−	0.794758i	$-0.707598\pi$
$293$	−20.7778			−1.21385			−0.606926	+	0.794758i	$0.707598\pi$
$294$		0			0
$295$	5.13307			0.298859
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	9.02558	−	15.6328i	0.522838	−	0.905582i
$299$	5.60817	+	9.71363i	0.324329	+	0.561754i
$300$		0			0
$301$	−25.1965	−	15.4048i	−1.45230	−	0.887918i
$302$	1.64766			0.0948124
$303$		0			0
$304$	2.69076	−	4.66053i	0.154326	−	0.267300i
$305$	−1.97296	+	3.41726i	−0.112971	+	0.195672i
$306$		0			0
$307$	−22.6768			−1.29424			−0.647118	−	0.762390i	$-0.724026\pi$
$307$	−22.6768			−1.29424			−0.647118	+	0.762390i	$0.724026\pi$
$308$	−0.0394951	+	1.56997i	−0.00225044	+	0.0894572i
$309$		0			0
$310$	−2.33482	−	4.04403i	−0.132609	−	0.229686i
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	−0.943477	−	0.331439i	$-0.892466\pi$
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	0.758773	+	0.651356i	$0.225799\pi$
$312$		0			0
$313$	−0.133074	−	0.230492i	−0.00752181	−	0.0130282i	0.862240	−	0.506500i	$-0.169061\pi$
$313$	−0.133074	−	0.230492i	−0.00752181	−	0.0130282i	−0.869762	+	0.493472i	$0.835728\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	7.86186	+	13.6171i	0.441566	+	0.764815i	0.997806	−	0.0662067i	$-0.0210897\pi$
$317$	7.86186	+	13.6171i	0.441566	+	0.764815i	−0.556240	+	0.831022i	$0.687756\pi$
$318$		0			0
$319$	1.83842	−	3.18424i	0.102932	−	0.178283i
$320$	0.296790	+	0.514055i	0.0165910	+	0.0287365i
$321$		0			0
$322$	−10.3655	+	5.64180i	−0.577645	+	0.314405i
$323$	−15.7195			−0.874654
$324$		0			0
$325$	5.84348	−	10.1212i	0.324138	−	0.561424i
$326$	−2.99115	+	5.18082i	−0.165664	+	0.286939i
$327$		0			0
$328$	−0.273346			−0.0150930
$329$	0.809243	−	32.1681i	0.0446150	−	1.77349i
$330$		0			0
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	0.971339	+	0.237697i	$0.0763925\pi$
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	−0.279818	+	0.960053i	$0.590274\pi$
$332$	−3.85087	+	6.66991i	−0.211344	+	0.366059i
$333$		0			0
$334$	−3.73025	−	6.46099i	−0.204110	−	0.353529i
$335$	1.13600			0.0620663
$336$		0			0
$337$	18.7339			1.02050			0.510249	−	0.860027i	$-0.329553\pi$
$337$	18.7339			1.02050			0.510249	+	0.860027i	$0.329553\pi$
$338$	3.33842	+	5.78231i	0.181586	+	0.314516i
$339$		0			0
$340$	0.866926	−	1.50156i	0.0470156	−	0.0814335i
$341$	2.33482	+	4.04403i	0.126438	+	0.218997i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$	11.1623			0.601828
$345$		0			0
$346$	−12.8296	+	22.2215i	−0.689722	+	1.19463i
$347$	11.2719	−	19.5235i	0.605106	−	1.04808i	−0.386928	−	0.922110i	$-0.626464\pi$
$347$	11.2719	−	19.5235i	0.605106	−	1.04808i	0.992035	−	0.125965i	$-0.0402028\pi$
$348$		0			0
$349$	−3.79086			−0.202920			−0.101460	−	0.994840i	$-0.532351\pi$
$349$	−3.79086			−0.202920			−0.101460	+	0.994840i	$0.532351\pi$
$350$	10.4911	+	6.41415i	0.560775	+	0.342851i
$351$		0			0
$352$	−0.296790	−	0.514055i	−0.0158189	−	0.0273992i
$353$	3.41741	−	5.91913i	0.181890	−	0.315043i	−0.760634	−	0.649181i	$-0.775112\pi$
$353$	3.41741	−	5.91913i	0.181890	−	0.315043i	0.942524	+	0.334138i	$0.108445\pi$
$354$		0			0
$355$	4.27694	+	7.40789i	0.226997	+	0.393170i
$356$	−12.4356			−0.659085
$357$		0			0
$358$	15.0364			0.794697
$359$	6.32237	+	10.9507i	0.333682	+	0.577954i	0.983231	−	0.182366i	$-0.0583755\pi$
$359$	6.32237	+	10.9507i	0.333682	+	0.577954i	−0.649549	+	0.760320i	$0.725042\pi$
$360$		0			0
$361$	−4.98035	+	8.62622i	−0.262124	+	0.454012i
$362$	0.0430937	+	0.0746406i	0.00226496	+	0.00392302i
$363$		0			0
$364$	5.84348	−	3.18054i	0.306282	−	0.166706i
$365$	4.69748			0.245877
$366$		0			0
$367$	−3.27188	+	5.66707i	−0.170791	+	0.295819i	−0.938697	−	0.344744i	$-0.887966\pi$
$367$	−3.27188	+	5.66707i	−0.170791	+	0.295819i	0.767906	+	0.640563i	$0.221299\pi$
$368$	2.23025	−	3.86291i	0.116260	−	0.201368i
$369$		0			0
$370$	0.593579			0.0308587
$371$	18.7163	−	10.1871i	0.971704	−	0.528887i
$372$		0			0
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	0.717784	−	0.696266i	$-0.245157\pi$
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	−0.961876	+	0.273486i	$0.911823\pi$
$374$	−0.866926	+	1.50156i	−0.0448277	+	0.0776438i
$375$		0			0
$376$	6.08113	+	10.5328i	0.313610	+	0.543189i
$377$	−15.5763			−0.802218
$378$		0			0
$379$	−7.27762			−0.373826			−0.186913	−	0.982376i	$-0.559848\pi$
$379$	−7.27762			−0.373826			−0.186913	+	0.982376i	$0.559848\pi$
$380$	−1.59718	−	2.76639i	−0.0819335	−	0.141913i
$381$		0			0
$382$	1.99115	−	3.44877i	0.101876	−	0.176454i
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	−0.990332	−	0.138717i	$-0.955702\pi$
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	0.375033	−	0.927011i	$-0.377631\pi$
$384$		0			0
$385$	0.795327	+	0.486253i	0.0405336	+	0.0247817i
$386$	6.78074			0.345130
$387$		0			0
$388$	5.86693	−	10.1618i	0.297848	−	0.515888i
$389$	−8.14913	+	14.1147i	−0.413177	+	0.715644i	−0.995235	−	0.0975035i	$-0.968914\pi$
$389$	−8.14913	+	14.1147i	−0.413177	+	0.715644i	0.582058	+	0.813147i	$0.302248\pi$
$390$		0			0
$391$	−13.0292			−0.658914
$392$	3.19076	+	6.23049i	0.161158	+	0.314688i
$393$		0			0
$394$	5.52918	+	9.57682i	0.278556	+	0.482473i
$395$	−2.74484	+	4.75420i	−0.138108	+	0.239210i
$396$		0			0
$397$	−6.08619	−	10.5416i	−0.305457	−	0.529067i	0.671906	−	0.740636i	$-0.265476\pi$
$397$	−6.08619	−	10.5416i	−0.305457	−	0.529067i	−0.977363	+	0.211569i	$0.932143\pi$
$398$	−5.61849			−0.281629
$399$		0			0
$400$	−4.64766			−0.232383
$401$	−16.6804	−	28.8914i	−0.832981	−	1.44277i	−0.895663	−	0.444733i	$-0.853299\pi$
$401$	−16.6804	−	28.8914i	−0.832981	−	1.44277i	0.0626819	−	0.998034i	$-0.480035\pi$
$402$		0			0
$403$	9.89104	−	17.1318i	0.492708	−	0.853395i
$404$	−0.811379	−	1.40535i	−0.0403676	−	0.0699187i
$405$		0			0
$406$	0.412155	−	16.3835i	0.0204549	−	0.813102i
$407$	−0.593579			−0.0294226
$408$		0			0
$409$	2.89037	−	5.00627i	0.142920	−	0.247544i	−0.785675	−	0.618639i	$-0.787684\pi$
$409$	2.89037	−	5.00627i	0.142920	−	0.247544i	0.928595	+	0.371095i	$0.121018\pi$
$410$	−0.0811263	+	0.140515i	−0.00400654	+	0.00693954i
$411$		0			0
$412$	6.38151			0.314395
$413$	−20.0957	+	10.9379i	−0.988846	+	0.538217i
$414$		0			0
$415$	2.28580	+	3.95912i	0.112205	+	0.194346i
$416$	−1.25729	+	2.17770i	−0.0616439	+	0.106770i
$417$		0			0
$418$	1.59718	+	2.76639i	0.0781205	+	0.135309i
$419$	30.8712			1.50816			0.754078	−	0.656784i	$-0.228084\pi$
$419$	30.8712			1.50816			0.754078	+	0.656784i	$0.228084\pi$
$420$		0			0
$421$	3.73385			0.181977			0.0909884	−	0.995852i	$-0.470997\pi$
$421$	3.73385			0.181977			0.0909884	+	0.995852i	$0.470997\pi$
$422$	9.66225	+	16.7355i	0.470351	+	0.814672i
$423$		0			0
$424$	−4.02704	+	6.97504i	−0.195570	+	0.338738i
$425$	6.78794	+	11.7570i	0.329263	+	0.570301i
$426$		0			0
$427$	0.442317	−	17.5825i	0.0214052	−	0.850877i
$428$	18.7089			0.904331
$429$		0			0
$430$	3.31284	−	5.73801i	0.159759	−	0.276711i
$431$	14.0979	−	24.4182i	0.679070	−	1.17618i	−0.296192	−	0.955128i	$-0.595717\pi$
$431$	14.0979	−	24.4182i	0.679070	−	1.17618i	0.975261	−	0.221055i	$-0.0709499\pi$
$432$		0			0
$433$	12.5438			0.602815			0.301407	−	0.953495i	$-0.402544\pi$
$433$	12.5438			0.602815			0.301407	+	0.953495i	$0.402544\pi$
$434$	17.7580	+	10.8570i	0.852410	+	0.521152i
$435$		0			0
$436$	−1.43346	−	2.48283i	−0.0686504	−	0.118906i
$437$	−12.0021	+	20.7883i	−0.574140	+	0.994440i
$438$		0			0
$439$	−13.0203	−	22.5519i	−0.621426	−	1.07634i	−0.989220	−	0.146434i	$-0.953220\pi$
$439$	−13.0203	−	22.5519i	−0.621426	−	1.07634i	0.367794	−	0.929907i	$-0.380113\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	−11.7865	−	20.4148i	−0.559992	−	0.969935i	−0.997496	−	0.0707186i	$-0.977471\pi$
$443$	−11.7865	−	20.4148i	−0.559992	−	0.969935i	0.437504	−	0.899216i	$-0.355863\pi$
$444$		0			0
$445$	−3.69076	+	6.39258i	−0.174959	+	0.303037i
$446$	12.6623	+	21.9317i	0.599575	+	1.03849i
$447$		0			0
$448$	−2.25729	−	1.38008i	−0.106647	−	0.0652027i
$449$	−13.6870			−0.645928			−0.322964	−	0.946411i	$-0.604679\pi$
$449$	−13.6870			−0.645928			−0.322964	+	0.946411i	$0.604679\pi$
$450$		0			0
$451$	0.0811263	−	0.140515i	0.00382009	−	0.00661659i
$452$	6.16012	−	10.6696i	0.289748	−	0.501857i
$453$		0			0
$454$	−4.81711			−0.226078
$455$	0.0993140	−	3.94782i	0.00465591	−	0.185077i
$456$		0			0
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	0.999648	+	0.0265293i	$0.00844554\pi$
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	−0.476849	+	0.878985i	$0.658221\pi$
$458$	4.64766	−	8.04999i	0.217171	−	0.376151i
$459$		0			0
$460$	−1.32383	−	2.29294i	−0.0617240	−	0.106909i
$461$	−7.97509			−0.371437			−0.185719	−	0.982603i	$-0.559461\pi$
$461$	−7.97509			−0.371437			−0.185719	+	0.982603i	$0.559461\pi$
$462$		0			0
$463$	28.7352			1.33544			0.667719	−	0.744413i	$-0.267271\pi$
$463$	28.7352			1.33544			0.667719	+	0.744413i	$0.267271\pi$
$464$	3.09718	+	5.36447i	0.143783	+	0.249039i
$465$		0			0
$466$	−0.0971780	+	0.168317i	−0.00450168	+	0.00779714i
$467$	−16.7829	−	29.0688i	−0.776619	−	1.34514i	−0.933880	−	0.357586i	$-0.883600\pi$
$467$	−16.7829	−	29.0688i	−0.776619	−	1.34514i	0.157261	−	0.987557i	$-0.449733\pi$
$468$		0			0
$469$	−4.44738	+	2.42066i	−0.205361	+	0.111775i
$470$	7.21926			0.333000
$471$		0			0
$472$	4.32383	−	7.48910i	0.199020	−	0.344714i
$473$	−3.31284	+	5.73801i	−0.152325	+	0.263834i
$474$		0			0
$475$	25.0115			1.14760
$476$	−0.194356	+	7.72582i	−0.00890829	+	0.354112i
$477$		0			0
$478$	6.82743	+	11.8255i	0.312279	+	0.540884i
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	−0.861801	−	0.507246i	$-0.830664\pi$
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	0.870188	+	0.492719i	$0.163997\pi$
$480$		0			0
$481$	1.25729	+	2.17770i	0.0573277	+	0.0992945i
$482$	−13.0000			−0.592134
$483$		0			0
$484$	−10.6477			−0.483985
$485$	−3.48249	−	6.03184i	−0.158132	−	0.273892i
$486$		0			0
$487$	−14.9538	+	25.9007i	−0.677621	+	1.17367i	0.298075	+	0.954543i	$0.403656\pi$
$487$	−14.9538	+	25.9007i	−0.677621	+	1.17367i	−0.975695	+	0.219131i	$0.929678\pi$
$488$	3.32383	+	5.75705i	0.150463	+	0.260609i
$489$		0			0
$490$	4.14980	+	0.208922i	0.187469	+	0.00943816i
$491$	−0.510317			−0.0230303			−0.0115151	−	0.999934i	$-0.503665\pi$
$491$	−0.510317			−0.0230303			−0.0115151	+	0.999934i	$0.503665\pi$
$492$		0			0
$493$	9.04689	−	15.6697i	0.407451	−	0.705726i
$494$	6.76615	−	11.7193i	0.304423	−	0.527277i
$495$		0			0
$496$	−7.86693			−0.353235
$497$	−32.5292	−	19.8879i	−1.45913	−	0.892095i
$498$		0			0
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	0.996486	−	0.0837597i	$-0.0266928\pi$
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	−0.570781	+	0.821102i	$0.693359\pi$
$500$	−2.86333	+	4.95943i	−0.128052	+	0.221792i
$501$		0			0
$502$	−9.77188	−	16.9254i	−0.436141	−	0.755418i
$503$	37.7807			1.68456			0.842280	−	0.539040i	$-0.181213\pi$
$503$	37.7807			1.68456			0.842280	+	0.539040i	$0.181213\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$	1.32383	+	2.29294i	0.0588515	+	0.101934i
$507$		0			0
$508$	−6.16731	+	10.6821i	−0.273630	+	0.473942i
$509$	−5.60817	−	9.71363i	−0.248578	−	0.430549i	0.714554	−	0.699581i	$-0.246630\pi$
$509$	−5.60817	−	9.71363i	−0.248578	−	0.430549i	−0.963131	+	0.269031i	$0.913296\pi$
$510$		0			0
$511$	−18.3904	+	10.0097i	−0.813542	+	0.442801i
$512$	1.00000			0.0441942
$513$		0			0
$514$	4.16372	−	7.21177i	0.183654	−	0.318097i
$515$	1.89397	−	3.28045i	0.0834582	−	0.144554i
$516$		0			0
$517$	−7.21926			−0.317503
$518$	−2.32383	+	1.26483i	−0.102103	+	0.0555736i
$519$		0			0
$520$	0.746304	+	1.29264i	0.0327276	+	0.0566859i
$521$	13.7360	−	23.7914i	0.601785	−	1.04232i	−0.390766	−	0.920490i	$-0.627790\pi$
$521$	13.7360	−	23.7914i	0.601785	−	1.04232i	0.992551	−	0.121831i	$-0.0388767\pi$
$522$		0			0
$523$	11.0919	+	19.2118i	0.485016	+	0.840072i	0.999852	−	0.0172166i	$-0.00548048\pi$
$523$	11.0919	+	19.2118i	0.485016	+	0.840072i	−0.514836	+	0.857289i	$0.672147\pi$
$524$	1.18716			0.0518613
$525$		0			0
$526$	17.0905			0.745179
$527$	11.4897	+	19.9007i	0.500498	+	0.866889i
$528$		0			0
$529$	1.55195	−	2.68805i	0.0674760	−	0.116872i
$530$	2.39037	+	4.14024i	0.103831	+	0.179841i
$531$		0			0
$532$	12.1477	+	7.42692i	0.526668	+	0.321998i
$533$	−0.687353			−0.0297726
$534$		0			0
$535$	5.55262	−	9.61742i	0.240061	−	0.415797i
$536$	0.956906	−	1.65741i	0.0413321	−	0.0715892i
$537$		0			0
$538$	−10.0144			−0.431751
$539$	−4.14980	−	0.208922i	−0.178745	−	0.00899893i
$540$		0			0
$541$	14.9246	+	25.8502i	0.641659	+	1.11139i	0.985062	+	0.172198i	$0.0550869\pi$
$541$	14.9246	+	25.8502i	0.641659	+	1.11139i	−0.343403	+	0.939188i	$0.611580\pi$
$542$	5.10457	−	8.84137i	0.219260	−	0.379770i
$543$		0			0
$544$	−1.46050	−	2.52967i	−0.0626186	−	0.108459i
$545$	−1.70175			−0.0728949
$546$		0			0
$547$	−17.6870			−0.756240			−0.378120	−	0.925757i	$-0.623429\pi$
$547$	−17.6870			−0.756240			−0.378120	+	0.925757i	$0.623429\pi$
$548$	1.26089	+	2.18393i	0.0538627	+	0.0932929i
$549$		0			0
$550$	1.37938	−	2.38915i	0.0588169	−	0.101874i
$551$	−16.6675	−	28.8690i	−0.710060	−	1.22986i
$552$		0			0
$553$	0.615366	−	24.4613i	0.0261680	−	1.04020i
$554$	19.3422			0.821772
$555$		0			0
$556$	2.45691	−	4.25549i	0.104196	−	0.180473i
$557$	−15.0651	+	26.0935i	−0.638328	+	1.10562i	0.347472	+	0.937690i	$0.387040\pi$
$557$	−15.0651	+	26.0935i	−0.638328	+	1.10562i	−0.985800	+	0.167926i	$0.946293\pi$
$558$		0			0
$559$	28.0685			1.18717
$560$	−1.37938	+	0.750780i	−0.0582894	+	0.0317262i
$561$		0			0
$562$	6.40136	+	11.0875i	0.270025	+	0.467697i
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	−0.819617	−	0.572912i	$-0.805814\pi$
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	0.905965	+	0.423353i	$0.139147\pi$
$564$		0			0
$565$	−3.65652	−	6.33327i	−0.153831	−	0.266443i
$566$	−16.3523			−0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	3.11849	+	5.40138i	0.130734	+	0.226437i	0.923960	−	0.382490i	$-0.124933\pi$
$569$	3.11849	+	5.40138i	0.130734	+	0.226437i	−0.793226	+	0.608927i	$0.791600\pi$
$570$		0			0
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	0.205266	+	0.978706i	$0.434194\pi$
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	−0.950218	+	0.311587i	$0.899139\pi$
$572$	−0.746304	−	1.29264i	−0.0312045	−	0.0540479i
$573$		0			0
$574$	0.0181877	−	0.722977i	0.000759140	−	0.0301765i
$575$	20.7309			0.864539
$576$		0			0
$577$	23.1388	−	40.0776i	0.963281	−	1.66845i	0.249118	−	0.968473i	$-0.419859\pi$
$577$	23.1388	−	40.0776i	0.963281	−	1.66845i	0.714164	−	0.699979i	$-0.246807\pi$
$578$	4.23385	−	7.33325i	0.176105	−	0.305023i
$579$		0			0
$580$	3.67684			0.152673
$581$	−17.3851	−	10.6290i	−0.721256	−	0.440966i
$582$		0			0
$583$	−2.39037	−	4.14024i	−0.0989990	−	0.171471i
$584$	3.95691	−	6.85356i	0.163738	−	0.283602i
$585$		0			0
$586$	10.3889	+	17.9941i	0.429162	+	0.743330i
$587$	2.26322			0.0934132			0.0467066	−	0.998909i	$-0.485127\pi$
$587$	2.26322			0.0934132			0.0467066	+	0.998909i	$0.485127\pi$
$588$		0			0
$589$	42.3360			1.74442
$590$	−2.56654	−	4.44537i	−0.105663	−	0.183013i
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−23.0979	−	40.0067i	−0.948515	−	1.64288i	−0.748555	−	0.663072i	$-0.769252\pi$
$593$	−23.0979	−	40.0067i	−0.948515	−	1.64288i	−0.199960	−	0.979804i	$-0.564081\pi$
$594$		0			0
$595$	3.91381	+	2.39285i	0.160451	+	0.0980974i
$596$	−18.0512			−0.739404
$597$		0			0
$598$	5.60817	−	9.71363i	0.229335	−	0.397220i
$599$	−8.39037	+	14.5325i	−0.342821	+	0.593784i	−0.984955	−	0.172808i	$-0.944716\pi$
$599$	−8.39037	+	14.5325i	−0.342821	+	0.593784i	0.642134	+	0.766592i	$0.278049\pi$
$600$		0			0
$601$	11.3992			0.464984			0.232492	−	0.972598i	$-0.425312\pi$
$601$	11.3992			0.464984			0.232492	+	0.972598i	$0.425312\pi$
$602$	−0.742705	+	29.5232i	−0.0302704	+	1.20328i
$603$		0			0
$604$	−0.823832	−	1.42692i	−0.0335212	−	0.0580605i
$605$	−3.16012	+	5.47348i	−0.128477	+	0.222529i
$606$		0			0
$607$	7.21420	+	12.4954i	0.292815	+	0.507171i	0.974474	−	0.224499i	$-0.0720745\pi$
$607$	7.21420	+	12.4954i	0.292815	+	0.507171i	−0.681659	+	0.731670i	$0.738741\pi$
$608$	−5.38151			−0.218249
$609$		0			0
$610$	3.94592			0.159765
$611$	15.2915	+	26.4857i	0.618629	+	1.07150i
$612$		0			0
$613$	12.2053	−	21.1403i	0.492969	−	0.853848i	−0.506998	−	0.861947i	$-0.669245\pi$
$613$	12.2053	−	21.1403i	0.492969	−	0.853848i	0.999967	+	0.00809942i	$0.00257815\pi$
$614$	11.3384	+	19.6387i	0.457581	+	0.792554i
$615$		0			0
$616$	1.37938	−	0.750780i	0.0555767	−	0.0302498i
$617$	48.9397			1.97024			0.985119	−	0.171876i	$-0.0549828\pi$
$617$	48.9397			1.97024			0.985119	+	0.171876i	$0.0549828\pi$
$618$		0			0
$619$	22.3296	−	38.6759i	0.897501	−	1.55452i	0.0668227	−	0.997765i	$-0.478714\pi$
$619$	22.3296	−	38.6759i	0.897501	−	1.55452i	0.830678	−	0.556753i	$-0.187953\pi$
$620$	−2.33482	+	4.04403i	−0.0937687	+	0.162412i
$621$		0			0
$622$	6.51459			0.261211
$623$	0.827430	−	32.8911i	0.0331503	−	1.31775i
$624$		0			0
$625$	−9.91955	−	17.1812i	−0.396782	−	0.687246i
$626$	−0.133074	+	0.230492i	−0.00531873	+	0.00921230i
$627$		0			0
$628$	3.30039	+	5.71644i	0.131700	+	0.228111i
$629$	−2.92101			−0.116468
$630$		0			0
$631$	33.2852			1.32506			0.662532	−	0.749034i	$-0.269482\pi$
$631$	33.2852			1.32506			0.662532	+	0.749034i	$0.269482\pi$
$632$	4.62422	+	8.00938i	0.183942	+	0.318596i
$633$		0			0
$634$	7.86186	−	13.6171i	0.312235	−	0.540806i
$635$	3.66079	+	6.34067i	0.145274	+	0.251622i
$636$		0			0
$637$	8.02344	+	15.6671i	0.317900	+	0.620754i
$638$	−3.67684			−0.145568
$639$		0			0
$640$	0.296790	−	0.514055i	0.0117316	−	0.0203198i
$641$	15.3940	−	26.6631i	0.608025	−	1.05313i	−0.383540	−	0.923524i	$-0.625295\pi$
$641$	15.3940	−	26.6631i	0.608025	−	1.05313i	0.991566	−	0.129606i	$-0.0413714\pi$
$642$		0			0
$643$	27.4690			1.08327			0.541637	−	0.840613i	$-0.317805\pi$
$643$	27.4690			1.08327			0.541637	+	0.840613i	$0.317805\pi$
$644$	10.0687	+	6.15585i	0.396761	+	0.242575i
$645$		0			0
$646$	7.85973	+	13.6134i	0.309237	+	0.535614i
$647$	6.63521	−	11.4925i	0.260857	−	0.451818i	−0.705613	−	0.708598i	$-0.749328\pi$
$647$	6.63521	−	11.4925i	0.260857	−	0.451818i	0.966470	+	0.256780i	$0.0826615\pi$
$648$		0			0
$649$	2.56654	+	4.44537i	0.100745	+	0.174496i
$650$	−11.6870			−0.458400
$651$		0			0
$652$	5.98229			0.234285
$653$	−8.57081	−	14.8451i	−0.335402	−	0.580933i	0.648160	−	0.761504i	$-0.275539\pi$
$653$	−8.57081	−	14.8451i	−0.335402	−	0.580933i	−0.983562	+	0.180571i	$0.942205\pi$
$654$		0			0
$655$	0.352336	−	0.610265i	0.0137669	−	0.0238450i
$656$	0.136673	+	0.236725i	0.00533619	+	0.00924255i
$657$		0			0
$658$	−28.2630	+	15.3832i	−1.10181	+	0.599701i
$659$	8.52179			0.331962			0.165981	−	0.986129i	$-0.446921\pi$
$659$	8.52179			0.331962			0.165981	+	0.986129i	$0.446921\pi$
$660$		0			0
$661$	−17.1680	+	29.7358i	−0.667757	+	1.15659i	0.310773	+	0.950484i	$0.399412\pi$
$661$	−17.1680	+	29.7358i	−0.667757	+	1.15659i	−0.978530	+	0.206105i	$0.933921\pi$
$662$	12.5811	−	21.7912i	0.488979	−	0.846937i
$663$		0			0
$664$	7.70175			0.298886
$665$	7.42315	−	4.04033i	0.287857	−	0.156677i
$666$		0			0
$667$	−13.8150	−	23.9282i	−0.534918	−	0.926505i
$668$	−3.73025	+	6.46099i	−0.144328	+	0.249983i
$669$		0			0
$670$	−0.568000	−	0.983804i	−0.0219437	−	0.0380077i
$671$	−3.94592			−0.152330
$672$		0			0
$673$	15.4031			0.593746			0.296873	−	0.954917i	$-0.404056\pi$
$673$	15.4031			0.593746			0.296873	+	0.954917i	$0.404056\pi$
$674$	−9.36693	−	16.2240i	−0.360800	−	0.624925i
$675$		0			0
$676$	3.33842	−	5.78231i	0.128401	−	0.222397i
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	0.786345	−	0.617788i	$-0.211971\pi$
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	−0.928192	+	0.372101i	$0.878638\pi$
$678$		0			0
$679$	26.4868	+	16.1937i	1.01647	+	0.621455i
$680$	−1.73385			−0.0664902
$681$		0			0
$682$	2.33482	−	4.04403i	0.0894050	−	0.154854i
$683$	−4.79893	+	8.31198i	−0.183626	+	0.318049i	−0.943113	−	0.332474i	$-0.892117\pi$
$683$	−4.79893	+	8.31198i	−0.183626	+	0.318049i	0.759487	+	0.650523i	$0.225450\pi$
$684$		0			0
$685$	1.49688			0.0571929
$686$	−16.6914	+	8.02472i	−0.637282	+	0.306385i
$687$		0			0
$688$	−5.58113	−	9.66679i	−0.212778	−	0.368543i
$689$	−10.1264	+	17.5394i	−0.385783	+	0.668197i
$690$		0			0
$691$	7.07227	+	12.2495i	0.269042	+	0.465994i	0.968615	−	0.248567i	$-0.0799597\pi$
$691$	7.07227	+	12.2495i	0.269042	+	0.465994i	−0.699573	+	0.714561i	$0.746626\pi$
$692$	25.6591			0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	−1.45837	−	2.52597i	−0.0553191	−	0.0958155i
$696$		0			0
$697$	0.399223	−	0.691475i	0.0151217	−	0.0261915i
$698$	1.89543	+	3.28298i	0.0717431	+	0.124263i
$699$		0			0
$700$	0.309243	−	12.2927i	0.0116883	−	0.464619i
$701$	−37.3753			−1.41164			−0.705822	−	0.708389i	$-0.749422\pi$
$701$	−37.3753			−1.41164			−0.705822	+	0.708389i	$0.749422\pi$
$702$		0			0
$703$	−2.69076	+	4.66053i	−0.101484	+	0.175775i
$704$	−0.296790	+	0.514055i	−0.0111857	+	0.0193742i
$705$		0			0
$706$	−6.83482			−0.257232
$707$	3.77102	−	2.05252i	0.141824	−	0.0771929i
$708$		0			0
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	0.947528	−	0.319673i	$-0.103573\pi$
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	−0.750609	+	0.660747i	$0.770240\pi$
$710$	4.27694	−	7.40789i	0.160511	−	0.278013i
$711$		0			0
$712$	6.21780	+	10.7695i	0.233022	+	0.403606i
$713$	35.0905			1.31415
$714$		0			0
$715$	−0.885981			−0.0331338
$716$	−7.51819	−	13.0219i	−0.280968	−	0.486651i
$717$		0			0
$718$	6.32237	−	10.9507i	0.235949	−	0.408675i
$719$	−1.11995	−	1.93981i	−0.0417670	−	0.0723426i	0.844386	−	0.535735i	$-0.179965\pi$
$719$	−1.11995	−	1.93981i	−0.0417670	−	0.0723426i	−0.886153	+	0.463392i	$0.846632\pi$
$720$		0			0
$721$	−0.424608	+	16.8786i	−0.0158132	+	0.628590i
$722$	9.96070			0.370699
$723$		0			0
$724$	0.0430937	−	0.0746406i	0.00160157	−	0.00277399i
$725$	−14.3946	+	24.9322i	−0.534604	+	0.925961i
$726$		0			0
$727$	−0.370045			−0.0137242			−0.00686211	−	0.999976i	$-0.502184\pi$
$727$	−0.370045			−0.0137242			−0.00686211	+	0.999976i	$0.502184\pi$
$728$	−5.67617	−	3.47033i	−0.210373	−	0.128619i
$729$		0			0
$730$	−2.34874	−	4.06813i	−0.0869307	−	0.150568i
$731$	−16.3025	+	28.2368i	−0.602971	+	1.04438i
$732$		0			0
$733$	−7.00953	−	12.1409i	−0.258903	−	0.448433i	0.707045	−	0.707168i	$-0.250028\pi$
$733$	−7.00953	−	12.1409i	−0.258903	−	0.448433i	−0.965948	+	0.258735i	$0.916694\pi$
$734$	6.54377			0.241535
$735$		0			0
$736$	−4.46050			−0.164416
$737$	0.568000	+	0.983804i	0.0209225	+	0.0362389i
$738$		0			0
$739$	13.3872	−	23.1874i	0.492458	−	0.852962i	−0.507504	−	0.861649i	$-0.669432\pi$
$739$	13.3872	−	23.1874i	0.492458	−	0.852962i	0.999962	+	0.00868705i	$0.00276521\pi$
$740$	−0.296790	−	0.514055i	−0.0109102	−	0.0188970i
$741$		0			0
$742$	−18.1804	−	11.1153i	−0.667425	−	0.408055i
$743$	−10.0934			−0.370290			−0.185145	−	0.982711i	$-0.559276\pi$
$743$	−10.0934			−0.370290			−0.185145	+	0.982711i	$0.559276\pi$
$744$		0			0
$745$	−5.35740	+	9.27928i	−0.196280	+	0.339967i
$746$	−4.71420	+	8.16524i	−0.172599	+	0.298951i
$747$		0			0
$748$	1.73385			0.0633959
$749$	−1.24484	+	49.4836i	−0.0454855	+	1.80809i
$750$		0			0
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	0.741655	−	0.670782i	$-0.234041\pi$
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	−0.951741	+	0.306901i	$0.900708\pi$
$752$	6.08113	−	10.5328i	0.221756	−	0.384092i
$753$		0			0
$754$	7.78813	+	13.4894i	0.283627	+	0.491256i
$755$	−0.978019			−0.0355938
$756$		0			0
$757$	−15.2484			−0.554214			−0.277107	−	0.960839i	$-0.589376\pi$
$757$	−15.2484			−0.554214			−0.277107	+	0.960839i	$0.589376\pi$
$758$	3.63881	+	6.30260i	0.132168	+	0.228921i
$759$		0			0
$760$	−1.59718	+	2.76639i	−0.0579357	+	0.100348i
$761$	−0.850874	−	1.47376i	−0.0308442	−	0.0534236i	0.850191	−	0.526474i	$-0.176486\pi$
$761$	−0.850874	−	1.47376i	−0.0308442	−	0.0534236i	−0.881035	+	0.473050i	$0.843153\pi$
$762$		0			0
$763$	6.66225	−	3.62619i	0.241190	−	0.131277i
$764$	−3.98229			−0.144074
$765$		0			0
$766$	−12.0416	+	20.8567i	−0.435082	+	0.753584i
$767$	10.8727	−	18.8320i	0.392589	−	0.679984i
$768$		0			0
$769$	−48.2422			−1.73966			−0.869829	−	0.493353i	$-0.835771\pi$
$769$	−48.2422			−1.73966			−0.869829	+	0.493353i	$0.835771\pi$
$770$	0.0234435	−	0.931900i	0.000844845	−	0.0335833i
$771$		0			0
$772$	−3.39037	−	5.87229i	−0.122022	−	0.211348i
$773$	−3.10243	+	5.37357i	−0.111587	+	0.193274i	−0.916410	−	0.400240i	$-0.868927\pi$
$773$	−3.10243	+	5.37357i	−0.111587	+	0.193274i	0.804823	+	0.593514i	$0.202260\pi$
$774$		0			0
$775$	−18.2814	−	31.6643i	−0.656688	−	1.13742i
$776$	−11.7339			−0.421221
$777$		0			0
$778$	16.2983			0.584321
$779$	−0.735508	−	1.27394i	−0.0263523	−	0.0456436i
$780$		0			0
$781$	−4.27694	+	7.40789i	−0.153041	+	0.265075i
$782$	6.51459	+	11.2836i	0.232961	+	0.403501i
$783$		0			0
$784$	3.80039	−	5.87852i	0.135728	−	0.209947i
$785$	3.91808			0.139842
$786$		0			0
$787$	−3.04883	+	5.28073i	−0.108679	+	0.188238i	−0.915235	−	0.402920i	$-0.867995\pi$
$787$	−3.04883	+	5.28073i	−0.108679	+	0.188238i	0.806556	+	0.591157i	$0.201329\pi$
$788$	5.52918	−	9.57682i	0.196969	−	0.341160i
$789$		0			0
$790$	5.48968			0.195314
$791$	27.8104	+	17.0029i	0.988824	+	0.604554i
$792$		0			0
$793$	8.35807	+	14.4766i	0.296804	+	0.514079i
$794$	−6.08619	+	10.5416i	−0.215991	+	0.374107i
$795$		0			0
$796$	2.80924	+	4.86575i	0.0995710	+	0.172462i
$797$	−12.4572			−0.441256			−0.220628	−	0.975358i	$-0.570811\pi$
$797$	−12.4572			−0.441256			−0.220628	+	0.975358i	$0.570811\pi$
$798$		0			0
$799$	−35.5261			−1.25682
$800$	2.32383	+	4.02499i	0.0821599	+	0.142305i
$801$		0			0
$802$	−16.6804	+	28.8914i	−0.589007	+	1.02019i
$803$	2.34874	+	4.06813i	0.0828852	+	0.143561i
$804$		0			0
$805$	6.15272	−	3.34886i	0.216855	−	0.118032i
$806$	−19.7821			−0.696794
$807$		0			0
$808$	−0.811379	+	1.40535i	−0.0285442	+	0.0494400i
$809$	2.81644	−	4.87822i	0.0990208	−	0.171509i	−0.812259	−	0.583297i	$-0.801762\pi$
$809$	2.81644	−	4.87822i	0.0990208	−	0.171509i	0.911280	+	0.411788i	$0.135096\pi$
$810$		0			0
$811$	−45.6414			−1.60269			−0.801344	−	0.598204i	$-0.795881\pi$
$811$	−45.6414			−1.60269			−0.801344	+	0.598204i	$0.795881\pi$
$812$	−14.3946	+	7.83483i	−0.505153	+	0.274949i
$813$		0			0
$814$	0.296790	+	0.514055i	0.0104025	+	0.0180176i
$815$	1.77548	−	3.07523i	0.0621924	−	0.107720i
$816$		0			0
$817$	30.0349	+	52.0220i	1.05079	+	1.82002i
$818$	−5.78074			−0.202119
$819$		0			0
$820$	0.162253			0.00566611
$821$	16.3473	+	28.3143i	0.570524	+	0.988176i	0.996512	+	0.0834476i	$0.0265931\pi$
$821$	16.3473	+	28.3143i	0.570524	+	0.988176i	−0.425988	+	0.904729i	$0.640074\pi$
$822$		0			0
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	−0.760591	−	0.649231i	$-0.775091\pi$
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	0.942546	+	0.334075i	$0.108424\pi$
$824$	−3.19076	−	5.52655i	−0.111155	−	0.192527i
$825$		0			0
$826$	19.5203	+	11.9345i	0.679199	+	0.415253i
$827$	−16.7060			−0.580925			−0.290463	−	0.956886i	$-0.593809\pi$
$827$	−16.7060			−0.580925			−0.290463	+	0.956886i	$0.593809\pi$
$828$		0			0
$829$	−13.1046	+	22.6978i	−0.455141	+	0.788327i	−0.998696	−	0.0510466i	$-0.983744\pi$
$829$	−13.1046	+	22.6978i	−0.455141	+	0.788327i	0.543556	+	0.839373i	$0.317078\pi$
$830$	2.28580	−	3.95912i	0.0793412	−	0.137423i
$831$		0			0
$832$	2.51459			0.0871777
$833$	−20.4212	−	1.02811i	−0.707553	−	0.0356219i
$834$		0			0
$835$	2.21420	+	3.83511i	0.0766256	+	0.132719i
$836$	1.59718	−	2.76639i	0.0552396	−	0.0956777i
$837$		0			0
$838$	−15.4356	−	26.7352i	−0.533214	−	0.923554i
$839$	22.3772			0.772548			0.386274	−	0.922384i	$-0.373762\pi$
$839$	22.3772			0.772548			0.386274	+	0.922384i	$0.373762\pi$
$840$		0			0
$841$	9.37005			0.323105
$842$	−1.86693	−	3.23361i	−0.0643385	−	0.111438i
$843$		0			0
$844$	9.66225	−	16.7355i	0.332588	−	0.576060i
$845$	−1.98162	−	3.43226i	−0.0681697	−	0.118073i
$846$		0			0
$847$	0.708466	−	28.1622i	0.0243432	−	0.967663i
$848$	8.05408			0.276578
$849$		0			0
$850$	6.78794	−	11.7570i	0.232824	−	0.403263i
$851$	−2.23025	+	3.86291i	−0.0764521	+	0.132419i
$852$		0			0
$853$	−9.92528			−0.339835			−0.169918	−	0.985458i	$-0.554350\pi$
$853$	−9.92528			−0.339835			−0.169918	+	0.985458i	$0.554350\pi$
$854$	−15.4481	+	8.40819i	−0.528621	+	0.287722i
$855$		0			0
$856$	−9.35447	−	16.2024i	−0.319729	−	0.553787i
$857$	3.89776	−	6.75112i	0.133145	−	0.230614i	−0.791742	−	0.610855i	$-0.790826\pi$
$857$	3.89776	−	6.75112i	0.133145	−	0.230614i	0.924887	+	0.380241i	$0.124159\pi$
$858$		0			0
$859$	−8.17111	−	14.1528i	−0.278795	−	0.482886i	0.692291	−	0.721619i	$-0.256602\pi$
$859$	−8.17111	−	14.1528i	−0.278795	−	0.482886i	−0.971085	+	0.238732i	$0.923268\pi$
$860$	−6.62568			−0.225934
$861$		0			0
$862$	−28.1957			−0.960349
$863$	−0.730252	−	1.26483i	−0.0248581	−	0.0430555i	0.853329	−	0.521373i	$-0.174580\pi$
$863$	−0.730252	−	1.26483i	−0.0248581	−	0.0430555i	−0.878187	+	0.478318i	$0.841247\pi$
$864$		0			0
$865$	7.61537	−	13.1902i	0.258930	−	0.448480i
$866$	−6.27188	−	10.8632i	−0.213127	−	0.369147i
$867$		0			0
$868$	0.523443	−	20.8073i	0.0177668	−	0.706247i
$869$	−5.48968			−0.186225
$870$		0			0
$871$	2.40623	−	4.16771i	0.0815319	−	0.141217i
$872$	−1.43346	+	2.48283i	−0.0485432	+	0.0840792i
$873$		0			0
$874$	24.0043			0.811957
$875$	−12.9267	−	7.90324i	−0.437004	−	0.267178i
$876$		0			0
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	0.885648	−	0.464357i	$-0.153715\pi$
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	−0.844969	+	0.534815i	$0.820381\pi$
$878$	−13.0203	+	22.5519i	−0.439415	+	0.761088i
$879$		0			0
$880$	0.176168	+	0.305132i	0.00593863	+	0.0102860i
$881$	18.9607			0.638802			0.319401	−	0.947620i	$-0.396518\pi$
$881$	18.9607			0.638802			0.319401	+	0.947620i	$0.396518\pi$
$882$		0			0
$883$	3.64008			0.122498			0.0612492	−	0.998123i	$-0.480492\pi$
$883$	3.64008			0.122498			0.0612492	+	0.998123i	$0.480492\pi$
$884$	−3.67257	−	6.36108i	−0.123522	−	0.213946i
$885$		0			0
$886$	−11.7865	+	20.4148i	−0.395974	+	0.685848i
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	0.584359	−	0.811495i	$-0.301346\pi$
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	−0.994955	+	0.100322i	$0.968013\pi$
$888$		0			0
$889$	−27.8429	−	17.0228i	−0.933820	−	0.570926i
$890$	7.38151			0.247429
$891$		0			0
$892$	12.6623	−	21.9317i	0.423964	−	0.734326i
$893$	−32.7257	+	56.6825i	−1.09512	+	1.89681i
$894$		0			0
$895$	−8.92528			−0.298339
$896$	−0.0665372	+	2.64491i	−0.00222285	+	0.0883604i
$897$		0			0
$898$	6.84348	+	11.8533i	0.228370	+	0.395548i
$899$	−24.3653	+	42.2019i	−0.812627	+	1.40751i
$900$		0			0
$901$	−11.7630	−	20.3742i	−0.391883	−	0.678762i
$902$	−0.162253			−0.00540242
$903$		0			0
$904$	−12.3202			−0.409765
$905$	−0.0255796	−	0.0443051i	−0.000850293	−	0.00147275i
$906$		0			0
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	−0.937234	−	0.348701i	$-0.886623\pi$
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	0.770601	+	0.637318i	$0.219956\pi$
$908$	2.40856	+	4.17174i	0.0799308	+	0.138444i
$909$		0			0
$910$	−3.46857	+	1.88790i	−0.114982	+	0.0625833i
$911$	22.8918			0.758440			0.379220	−	0.925306i	$-0.376192\pi$
$911$	22.8918			0.758440			0.379220	+	0.925306i	$0.376192\pi$
$912$		0			0
$913$	−2.28580	+	3.95912i	−0.0756489	+	0.131028i
$914$	11.1762	−	19.3577i	0.369675	−	0.640296i
$915$		0			0
$916$	−9.29533			−0.307126
$917$	−0.0789903	+	3.13993i	−0.00260849	+	0.103690i
$918$		0			0
$919$	10.8910	+	18.8638i	0.359262	+	0.622261i	0.987838	−	0.155488i	$-0.0496950\pi$
$919$	10.8910	+	18.8638i	0.359262	+	0.622261i	−0.628575	+	0.777749i	$0.716362\pi$
$920$	−1.32383	+	2.29294i	−0.0436454	+	0.0755961i
$921$		0			0
$922$	3.98755	+	6.90663i	0.131323	+	0.227458i
$923$	36.2370			1.19275
$924$		0			0
$925$	4.64766			0.152814
$926$	−14.3676	−	24.8854i	−0.472149	−	0.817785i
$927$		0			0
$928$	3.09718	−	5.36447i	0.101670	−	0.176097i
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	−0.998975	−	0.0452622i	$-0.985588\pi$
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	0.460289	−	0.887769i	$-0.347746\pi$
$930$		0			0
$931$	−20.4518	+	31.6354i	−0.670282	+	1.03681i
$932$	0.194356			0.00636634
$933$		0			0
$934$	−16.7829	+	29.0688i	−0.549152	+	0.951160i
$935$	0.514589	−	0.891294i	0.0168289	−	0.0291484i
$936$		0			0
$937$	−8.78074			−0.286854			−0.143427	−	0.989661i	$-0.545812\pi$
$937$	−8.78074			−0.286854			−0.143427	+	0.989661i	$0.545812\pi$
$938$	4.32004	+	2.64121i	0.141054	+	0.0862387i
$939$		0			0
$940$	−3.60963	−	6.25206i	−0.117733	−	0.203920i
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	−0.829161	−	0.559010i	$-0.811181\pi$
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	0.898697	+	0.438570i	$0.144515\pi$
$942$		0			0
$943$	−0.609631	−	1.05591i	−0.0198523	−	0.0343852i
$944$	−8.64766			−0.281457
$945$		0			0
$946$	6.62568			0.215420
$947$	−11.5292	−	19.9691i	−0.374648	−	0.648909i	0.615626	−	0.788038i	$-0.288903\pi$
$947$	−11.5292	−	19.9691i	−0.374648	−	0.648909i	−0.990274	+	0.139129i	$0.955570\pi$
$948$		0			0
$949$	9.94999	−	17.2339i	0.322990	−	0.559436i
$950$	−12.5057	−	21.6606i	−0.405740	−	0.702762i
$951$		0			0
$952$	6.78794	−	3.69459i	0.219998	−	0.119742i
$953$	36.5552			1.18414			0.592070	−	0.805886i	$-0.298311\pi$
$953$	36.5552			1.18414			0.592070	+	0.805886i	$0.298311\pi$
$954$		0			0
$955$	−1.18190	+	2.04712i	−0.0382455	+	0.0662431i
$956$	6.82743	−	11.8255i	0.220815	−	0.382463i
$957$		0			0
$958$	−0.367120			−0.0118611
$959$	−5.86021	+	3.18964i	−0.189236	+	0.102999i
$960$		0			0
$961$	−15.4443	−	26.7502i	−0.498202	−	0.862911i
$962$	1.25729	−	2.17770i	0.0405368	−	0.0702118i
$963$		0			0
$964$	6.50000	+	11.2583i	0.209351	+	0.362606i
$965$	−4.02491			−0.129566
$966$		0			0
$967$	−53.5438			−1.72185			−0.860926	−	0.508731i	$-0.830115\pi$
$967$	−53.5438			−1.72185			−0.860926	+	0.508731i	$0.830115\pi$
$968$	5.32383	+	9.22115i	0.171114	+	0.296379i
$969$		0			0
$970$	−3.48249	+	6.03184i	−0.111816	+	0.193671i
$971$	15.9897	+	27.6949i	0.513133	+	0.888773i	0.999884	+	0.0152321i	$0.00484870\pi$
$971$	15.9897	+	27.6949i	0.513133	+	0.888773i	−0.486751	+	0.873541i	$0.661818\pi$
$972$		0			0
$973$	11.0919	+	6.78146i	0.355591	+	0.217403i
$974$	29.9076			0.958300
$975$		0			0
$976$	3.32383	−	5.75705i	0.106393	−	0.184279i
$977$	−13.7104	+	23.7471i	−0.438635	+	0.759738i	−0.997584	−	0.0694638i	$-0.977871\pi$
$977$	−13.7104	+	23.7471i	−0.438635	+	0.759738i	0.558950	+	0.829202i	$0.311204\pi$
$978$		0			0
$979$	−7.38151			−0.235914
$980$	−1.89397	−	3.69829i	−0.0605006	−	0.118138i
$981$		0			0
$982$	0.255158	+	0.441947i	0.00814243	+	0.0141031i
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.184471	+	0.982838i	$0.559057\pi$
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.758927	+	0.651175i	$0.774276\pi$
$984$		0			0
$985$	−3.28201	−	5.68460i	−0.104573	−	0.181126i
$986$	−18.0938			−0.576223
$987$		0			0
$988$	−13.5323			−0.430520
$989$	24.8946	+	43.1188i	0.791604	+	1.37110i
$990$		0			0
$991$	6.41887	−	11.1178i	0.203902	−	0.353169i	−0.745880	−	0.666080i	$-0.767971\pi$
$991$	6.41887	−	11.1178i	0.203902	−	0.353169i	0.949782	+	0.312911i	$0.101304\pi$
$992$	3.93346	+	6.81296i	0.124888	+	0.216312i
$993$		0			0
$994$	−0.958848	+	38.1151i	−0.0304128	+	1.20894i
$995$	3.33502			0.105727
$996$		0			0
$997$	2.89037	−	5.00627i	0.0915389	−	0.158550i	−0.816620	−	0.577176i	$-0.804155\pi$
$997$	2.89037	−	5.00627i	0.0915389	−	0.158550i	0.908159	+	0.418626i	$0.137488\pi$
$998$	9.50953	−	16.4710i	0.301019	−	0.521380i
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.l.487.2		6
3.2	odd	2		1134.2.g.m.487.2		6
7.2	even	3	inner	1134.2.g.l.163.2		6
7.3	odd	6		7938.2.a.bz.1.2		3
7.4	even	3		7938.2.a.ca.1.2		3
9.2	odd	6		126.2.h.d.67.2	yes	6
9.4	even	3		378.2.e.d.235.2		6
9.5	odd	6		126.2.e.c.25.2	✓	6
9.7	even	3		378.2.h.c.361.2		6
21.2	odd	6		1134.2.g.m.163.2		6
21.11	odd	6		7938.2.a.bv.1.2		3
21.17	even	6		7938.2.a.bw.1.2		3
36.7	odd	6		3024.2.t.h.1873.2		6
36.11	even	6		1008.2.t.h.193.2		6
36.23	even	6		1008.2.q.g.529.2		6
36.31	odd	6		3024.2.q.g.2881.2		6
63.2	odd	6		126.2.e.c.121.2	yes	6
63.4	even	3		2646.2.f.l.883.2		6
63.5	even	6		882.2.h.p.79.2		6
63.11	odd	6		882.2.f.n.589.1		6
63.13	odd	6		2646.2.e.p.2125.2		6
63.16	even	3		378.2.e.d.37.2		6
63.20	even	6		882.2.h.p.67.2		6
63.23	odd	6		126.2.h.d.79.2	yes	6
63.25	even	3		2646.2.f.l.1765.2		6
63.31	odd	6		2646.2.f.m.883.2		6
63.32	odd	6		882.2.f.n.295.1		6
63.34	odd	6		2646.2.h.o.361.2		6
63.38	even	6		882.2.f.o.589.3		6
63.40	odd	6		2646.2.h.o.667.2		6
63.41	even	6		882.2.e.o.655.2		6
63.47	even	6		882.2.e.o.373.2		6
63.52	odd	6		2646.2.f.m.1765.2		6
63.58	even	3		378.2.h.c.289.2		6
63.59	even	6		882.2.f.o.295.3		6
63.61	odd	6		2646.2.e.p.1549.2		6
252.23	even	6		1008.2.t.h.961.2		6
252.79	odd	6		3024.2.q.g.2305.2		6
252.191	even	6		1008.2.q.g.625.2		6
252.247	odd	6		3024.2.t.h.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	9.5	odd	6
126.2.e.c.121.2	yes	6	63.2	odd	6
126.2.h.d.67.2	yes	6	9.2	odd	6
126.2.h.d.79.2	yes	6	63.23	odd	6
378.2.e.d.37.2		6	63.16	even	3
378.2.e.d.235.2		6	9.4	even	3
378.2.h.c.289.2		6	63.58	even	3
378.2.h.c.361.2		6	9.7	even	3
882.2.e.o.373.2		6	63.47	even	6
882.2.e.o.655.2		6	63.41	even	6
882.2.f.n.295.1		6	63.32	odd	6
882.2.f.n.589.1		6	63.11	odd	6
882.2.f.o.295.3		6	63.59	even	6
882.2.f.o.589.3		6	63.38	even	6
882.2.h.p.67.2		6	63.20	even	6
882.2.h.p.79.2		6	63.5	even	6
1008.2.q.g.529.2		6	36.23	even	6
1008.2.q.g.625.2		6	252.191	even	6
1008.2.t.h.193.2		6	36.11	even	6
1008.2.t.h.961.2		6	252.23	even	6
1134.2.g.l.163.2		6	7.2	even	3	inner
1134.2.g.l.487.2		6	1.1	even	1	trivial
1134.2.g.m.163.2		6	21.2	odd	6
1134.2.g.m.487.2		6	3.2	odd	2
2646.2.e.p.1549.2		6	63.61	odd	6
2646.2.e.p.2125.2		6	63.13	odd	6
2646.2.f.l.883.2		6	63.4	even	3
2646.2.f.l.1765.2		6	63.25	even	3
2646.2.f.m.883.2		6	63.31	odd	6
2646.2.f.m.1765.2		6	63.52	odd	6
2646.2.h.o.361.2		6	63.34	odd	6
2646.2.h.o.667.2		6	63.40	odd	6
3024.2.q.g.2305.2		6	252.79	odd	6
3024.2.q.g.2881.2		6	36.31	odd	6
3024.2.t.h.289.2		6	252.247	odd	6
3024.2.t.h.1873.2		6	36.7	odd	6
7938.2.a.bv.1.2		3	21.11	odd	6
7938.2.a.bw.1.2		3	21.17	even	6
7938.2.a.bz.1.2		3	7.3	odd	6
7938.2.a.ca.1.2		3	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1134.2.g.l.487.2

Level	$1134$
Weight	$2$
Character	1134.487
Analytic conductor	$9.055$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$